The type of the map keys.

The type of maps from type key to type 'a.

The empty map.

Test whether a map is empty or not.

mem x m returns true if m contains a binding for x, and false otherwise.

add x y m returns a map containing the same bindings as m, plus a binding of x to y. If x was already bound in m to a value that is physically equal to y, m is returned unchanged (the result of the function is then physically equal to m). Otherwise, the previous binding of x in m disappears.

• before 4.03

  Physical equality was not ensured.

singleton x y returns the one-element map that contains a binding y for x.

• since 3.12.0

remove x m returns a map containing the same bindings as m, except for x which is unbound in the returned map. If x was not in m, m is returned unchanged (the result of the function is then physically equal to m).

• before 4.03

  Physical equality was not ensured.

merge f m1 m2 computes a map whose keys is a subset of keys of m1 and of m2. The presence of each such binding, and the corresponding value, is determined with the function f. In terms of the find_opt operation, we have find_opt x (merge f m1 m2) = f (find_opt x m1) (find_opt x m2) for any key x, provided that f None None = None.

• since 3.12.0

union f m1 m2 computes a map whose keys is the union of keys of m1 and of m2. When the same binding is defined in both arguments, the function f is used to combine them. This is a special case of merge: union f m1 m2 is equivalent to merge f' m1 m2, where

• f' None None = None
• f' (Some v) None = Some v
• f' None (Some v) = Some v
• f' (Some v1) (Some v2) = f v1 v2

• since 4.03.0

Total ordering between maps. The first argument is a total ordering used to compare data associated with equal keys in the two maps.

equal cmp m1 m2 tests whether the maps m1 and m2 are equal, that is, contain equal keys and associate them with equal data. cmp is the equality predicate used to compare the data associated with the keys.

iter f m applies f to all bindings in map m. f receives the key as first argument, and the associated value as second argument. The bindings are passed to f in increasing order with respect to the ordering over the type of the keys.

fold f m a computes (f kN dN ... (f k1 d1 a)...), where k1 ... kN are the keys of all bindings in m (in increasing order), and d1 ... dN are the associated data.

for_all p m checks if all the bindings of the map satisfy the predicate p.

• since 3.12.0

exists p m checks if at least one binding of the map satisfies the predicate p.

• since 3.12.0

filter p m returns the map with all the bindings in m that satisfy predicate p. If p satisfies every binding in m, m is returned unchanged (the result of the function is then physically equal to m)

• since 3.12.0

• before 4.03

  Physical equality was not ensured.

partition p m returns a pair of maps (m1, m2), where m1 contains all the bindings of s that satisfy the predicate p, and m2 is the map with all the bindings of s that do not satisfy p.

• since 3.12.0

Return the number of bindings of a map.

• since 3.12.0

Return the height of the tree encodin the map. NOTE THAT: two maps that are equal may have a different height.

• since now

Return the list of all bindings of the given map. The returned list is sorted in increasing order with respect to the ordering Ord.compare, where Ord is the argument given to Map.Make.

• since 3.12.0

Return the smallest binding of the given map (with respect to the Ord.compare ordering), or raise Not_found if the map is empty.

• since 3.12.0

Return the smallest binding of the given map (with respect to the Ord.compare ordering), or None if the map is empty.

• since 4.05

Same as Map.S.min_binding, but returns the largest binding of the given map.

• since 3.12.0

Same as Map.S.min_binding_opt, but returns the largest binding of the given map.

• since 4.05

Return one binding of the given map, or raise Not_found if the map is empty. Which binding is chosen is unspecified, but equal bindings will be chosen for equal maps.

• since 3.12.0

Return one binding of the given map, or None if the map is empty. Which binding is chosen is unspecified, but equal bindings will be chosen for equal maps.

• since 4.05

split x m returns a triple (l, data, r), where l is the map with all the bindings of m whose key is strictly less than x; r is the map with all the bindings of m whose key is strictly greater than x; data is None if m contains no binding for x, or Some v if m binds v to x.

• since 3.12.0

find x m returns the current binding of x in m, or raises Not_found if no such binding exists.

find_opt x m returns Some v if the current binding of x in m is v, or None if no such binding exists.

• since 4.05

find_first f m, where f is a monotonically increasing function, returns the binding of m with the lowest key k such that f k, or raises Not_found if no such key exists.

For example, find_first (fun k -> Ord.compare k x >= 0) m will return the first binding k, v of m where Ord.compare k x >= 0 (intuitively: k >= x), or raise Not_found if x is greater than any element of m.

• since 4.05

find_first_opt f m, where f is a monotonically increasing function, returns an option containing the binding of m with the lowest key k such that f k, or None if no such key exists.

• since 4.05

find_last f m, where f is a monotonically decreasing function, returns the binding of m with the highest key k such that f k, or raises Not_found if no such key exists.

• since 4.05

find_last_opt f m, where f is a monotonically decreasing function, returns an option containing the binding of m with the highest key k such that f k, or None if no such key exists.

• since 4.05

map f m returns a map with same domain as m, where the associated value a of all bindings of m has been replaced by the result of the application of f to a. The bindings are passed to f in increasing order with respect to the ordering over the type of the keys.

Same as Map.S.map, but the function receives as arguments both the key and the associated value for each binding of the map.